Attitude dynamics and control of a compound solar sail

We consider attitude dynamics of a sailcraft that consists of a large parabolic surface which concentrates the solar radiation pressure on a small flat mirror. The control effort in such system is produced by rotation of the small mirror with respect to the parabolic surface. The sail axis is supposed to be oriented along the sun direction. We develop a model of the attitude dynamics for a non-ideal sailcraft, deducing the expressions for solar radiation force and torque valid also in the case of misalignment of the sail axis from the sun direction. Analysis of attitude stability of the sailcraft shows that for some shape of the collector with non-ideal optical properties its symmetry axis is stable with respect to the sun-sailcraft direction. We study the effect of rotating collector on the stability of the sailcraft. Considering a system of small vanes installed symmetrically around the sailcraft, we prove that the angular motion is controllable for any mission that does not require fast trajectory maneuvers.